相关论文: What Is Boolean Valued Analysis?

The analysis of time variability, whether fast variations on time scales well below the second or slow changes over years, is becoming more and more important in high-energy astronomy. Many sophisticated tools are available for data…

These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.

Scaled Boolean algebras are a category of mathematical objects that arose from attempts to understand why the conventional rules of probability should hold when probabilities are construed, not as frequencies or proportions or the like, but…

A brief introduction to geometric valuation theory is given. The focus is on classification results for valuations on convex bodies and on function spaces.

A number of topics in analysis are discussed, with emphasis on basic principles. There is some overlap with "Elements of linear and real analysis" (arXiv:math/0108030), with numerous changes in content and presentation since then.

The weak value of a variable O is a description of an effective interaction with that variable in the limit of weak coupling. It is particularly important for a pre- and post-selected quantum system.

The subject of this textbook is the analysis of Boolean functions. Roughly speaking, this refers to studying Boolean functions $f : \{0,1\}^n \to \{0,1\}$ via their Fourier expansion and other analytic means. Boolean functions are perhaps…

Boolean expressions are major focus of specifications and they are very much prone to introduction of faults, this survey presents various fault based testing techniques. It identifies that the techniques differ in their fault detection…

The paper presents several approaches to generalized blockmodeling of valued networks, where values of the ties are assumed to be measured on at least interval scale. The first approach is a straightforward generalization of the generalized…

Boolean calculus has been studied extensively in the past in the context of switching circuits, error-correcting codes etc. This work generalizes several approaches to defining a differential calculus for Boolean functions. A unified theory…

We discuss ways in which tools from topology can be used to derive lower bounds for the circuit complexity of Boolean functions.

This short note reviews briefly three algorithms for finding the set of dispensable variables of a boolean formula. The presentation is light on proofs and heavy on intuitions.

Recent results on the analytical evaluation of double-box Feynman integrals and the corresponding methods of evaluation are briefly reviewed.

This study presents a generalization for a method examining the correlation function of an arbitrary system with interactions in an Ising model to obtain a value of correlation between two arbitrary points on a network. The establishment of…

This note gives an overview of the BV formalism in its various incarnations and applications.

Boolean networks are special types of finite state time-discrete dynamical systems. A Boolean network can be described by a function from an n-dimensional vector space over the field of two elements to itself. A fundamental problem in…

The notion of variation is introduced for the Boolean set and based on which Boolean logic backpropagation principle is developed. Using this concept, deep models can be built with weights and activations being Boolean numbers and operated…

A detailed and formal account of polarization measurements using Bayesian analysis is given based on the assumption of gaussian error for the Stokes parameters. This analysis is crucial for the measurement of the polarization degree and…

Deep learning is computationally intensive, with significant efforts focused on reducing arithmetic complexity, particularly regarding energy consumption dominated by data movement. While existing literature emphasizes inference, training…

Let K be a field. For a given valuation on K[x], we determine the structure of its graded algebra and describe its set of key polynomials, in terms of any given key polynomial of minimal degree. We also characterize valuations not admitting…